What Is the Difference Between an Interior & Exterior Angle?

Basic Angle Properties

• Generally, an angle is created by two lines which meet at a point, often called a vertex. Angles have several properties that are predictable and calculable through the use of trigonometry. This is because an angle is really two side of a triangle whose third side has not been drawn. Angles are often measured in degrees for building and remodeling, but the unit of radians may be used as well. The radian represents the distance created by the angle when it is superimposed onto a circle.

Angle Measurement

• Angles are measured with the assumption that they represent an area swept out by a ray or line through an area of no more than 360 degrees. This 360-degree limit imposes a certain amount of unused area. The swept area is the interior angle measure. The unused area, or area outside the lines, is the exterior angle. Therefore, the interior and exterior angles must add up to 360 degrees.

Proportionality of Angle Sides

• Due to the limiting measure, there exists a proportionality between the angles. As the interior angle grows the exterior angles lessens, conversely, the exterior angle grows as the interior angle lessens. This property allows for one or the other to be determined with great accuracy using the other. This is especially handy when one of the angles cannot be directly measured due to obstruction.

Uses

• The interior and exterior angles may be used to deduce certain properties of structures. For example, the law of sines and the law of cosines allows for the distances of the lines and their angles to be determined from only one interior angle and a couple of side lengths or several angles and one side length. This is often used in the profession of surveying building sites.